{
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   "cell_type": "markdown",
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    "<img src=\"https://raw.githubusercontent.com/Qiskit/qiskit-tutorials/master/images/qiskit-heading.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"500 px\" align=\"left\">"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Advanced Randomized Benchmarking Methods\n",
    "\n",
    "### Contributors\n",
    "\n",
    "Shelly Garion$^{1}$ and David McKay$^{2}$\n",
    "\n",
    "1. IBM Research Haifa, Haifa University Campus, Mount Carmel Haifa, Israel\n",
    "2. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "**Randomized benchmarking (RB)** is a scalable technique for measuring the average gate error. Variants of the randomized benchmarking protocol provide a wide variety of information about noise parameters, including error rates for specific gates,  leakage rates, coherence errors and others.\n",
    "\n",
    "In this tutorial the following advanced RB methods are described:\n",
    "\n",
    "- **Inteleved RB** benchmarking individual Clifford gates via randomization. The protocol estimates the gate error of the given Clifford. The protocol is described in [1]. \n",
    "\n",
    "- **Purity RB:** quantifies how coherent the errors are. The protocol is based on [2,3]. \n",
    "\n",
    "\n",
    "### References\n",
    "\n",
    "[1] Easwar Magesan, Jay M. Gambetta, B. R. Johnson, Colm A. Ryan, Jerry M. Chow, Seth T. Merkel, Marcus P. da Silva, George A. Keefe, Mary B. Rothwell, Thomas A. Ohki, Mark B. Ketchen, and M. Steffen, *Efficient measurement of quantum gate error by interleaved randomized benchmarking*, https://arxiv.org/abs/1203.4550\n",
    "\n",
    "[2] Joel Wallman, Chris Granade, Robin Harper, and Steven T. Flammia, *Estimating the Coherence of Noise*, https://arxiv.org/abs/1503.07865\n",
    "\n",
    "[3] David C. McKay, Stefan Filipp, Antonio Mezzacapo, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta, *A universal gate for fixed-frequency qubits via a tunable bus*, https://arxiv.org/abs/1604.03076\n",
    "\n",
    "\n",
    "We should first import the relevant qiskit classes for the demonstration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   },
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   "source": [
    "#Import general libraries (needed for functions)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython import display\n",
    "\n",
    "#Import the RB Functions\n",
    "import qiskit.ignis.verification.randomized_benchmarking as rb\n",
    "\n",
    "#Import Qiskit classes classes\n",
    "import qiskit\n",
    "from qiskit.providers.aer import noise\n",
    "from qiskit.providers.aer.noise.errors.standard_errors import depolarizing_error, coherent_unitary_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interleaved RB protocol\n",
    "\n",
    "To benchmark the given Clifford element $C$, which has an associated noise operator $\\Lambda _C$, we fix an initial state $\\psi$ and perform the following steps:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Implement standard randomized benchmarking\n",
    "\n",
    "For details see: https://github.com/Qiskit/qiskit-tutorials-community/blob/master/ignis/RB_overview.ipynb\n",
    "\n",
    "We also briefy summarize it here.\n",
    "\n",
    "For various values of $m$, choose $K$ sequences of random gates where the first $m$ gates are chosen uniformly at random\n",
    "from the $n$-qubit Clifford group. The $(m+1)$th gate is chosen to be the inverse of the composition of the first $m$ random gates and can be found efficiently by the Gottesman-Knill theorem.\n",
    "\n",
    "Assuming each Clifford element $C_{i_j}$ for each step $j$ has some associated error, $\\Lambda_{i_j}$ , the sequence of gates is modeled by\n",
    "$$ S_{{\\bf i}_m} = \\Lambda_{i_{m+1}} \\circ C_{i_{m+1}} \\circ \\left( \\bigcirc_{j=1}^m [\\Lambda_{i_j} \\circ C_{i_j}]\\right),$$\n",
    "where ${\\bf i}_m = (i_1,\\dots,i_m)$ and $i_{m+1}$ is uniquely determined by ${\\bf i}_m$.\n",
    "\n",
    "Next, measure the probability that the initial state is not changed by the sequence, $Tr[E_{\\psi} S_{{\\bf i}_m}(\\rho_\\psi)]$, which is called the *survival probability*. Here $\\rho_\\psi$ is a quantum state that takes into\n",
    "account state-preparation errors and $E_\\psi$ is the positive operator valued measure element that takes into account\n",
    "measurement errors. In the ideal (noise-free) case the survival probability will be 1 for each sequence. \n",
    "\n",
    "Averaging the survival probability over the $K$ sequences gives the sequence *fidelity* $F_{seq}(m,\\psi)$ and a fit to the model:\n",
    "$$F_{seq}(m,\\psi) = A \\alpha^m + B$$\n",
    "gives the depolarizing parameter $\\alpha$. \n",
    "The average *error rate per a Clifford gate (EPC)* is given by \n",
    "$r = \\frac{d-1}{d}(1-\\alpha)$, where $d=2^n$.\n",
    "The coefficients $A$ and $B$ absorb the state preparation and measurement errors as well as the error on the final gate."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Step 2: Generate the interleaved RB sequences\n",
    "\n",
    "Choose $K$ sequences of Clifford elements where the first Clifford $C_{i_1}$ in each sequence is chosen uniformly at random from the $n$-qubit Clifford group, the second is always chosen to be $C$, and alternate between uniformly random Clifford elements and deterministic $C$ up to the $m$th random gate. The $(m+1)$th gate is chosen to be the inverse of the composition of the first $m$ random gates and $m$ interlaced $C$ gates.\n",
    "\n",
    "The superoperator representing the sequence is:\n",
    "$$ \\mathcal{V}_{{\\bf i}_m} = \\Lambda_{i_{m+1}} \\circ C_{i_{m+1}} \\circ \\left( \\bigcirc_{j=1}^m [C \\circ \\Lambda_C \\circ \\Lambda_{i_j} \\circ C_{i_j}]\\right),$$\n",
    "\n",
    "For each of the $K$ sequences, measure the survival probability $Tr[E_{\\psi} \\mathcal{V}_{{\\bf i}_m}(\\rho_\\psi)]$ and average over the $K$ random sequences to find the new sequence fidelity $F_{\\overline{seq}}(m,\\psi)$.\n",
    "\n",
    "Fit $F_{\\overline{seq}}(m,\\psi)$ to one of the model to obtain the depolarizing parameter $\\alpha_C$, as before.\n",
    "\n",
    "\n",
    "For example, we generate below sequences of 2-qubit Clifford circuits."
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Number of qubits\n",
    "nQ = 2\n",
    "#There are 2 qubits: Q0,Q1.\n",
    "rb_opts = {}\n",
    "#Number of Cliffords in the sequence (start, stop, steps)\n",
    "rb_opts['length_vector'] = np.arange(1,200,20)\n",
    "#Number of seeds (random sequences)\n",
    "rb_opts['nseeds'] = 5\n",
    "#Default pattern\n",
    "rb_opts['rb_pattern'] = [[0,1]]\n",
    "#Interleaved Clifford gates (cx gate)\n",
    "rb_opts['interleaved_gates'] =  [['cx 0 1']]\n",
    "\n",
    "rb_original_circs, xdata, rb_interleaved_circs = rb.randomized_benchmarking_seq(**rb_opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we print the circuit corresponding to the first original and interleaved RB sequences:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───┐┌───┐          ┌─────┐┌───┐      ░ ┌───┐ ┌───┐           ┌─────┐»\n",
      "qr_0: |0>┤ H ├┤ S ├───────■──┤ Sdg ├┤ H ├──────░─┤ H ├─┤ S ├────────■──┤ Sdg ├»\n",
      "         ├───┤├───┤┌───┐┌─┴─┐└┬───┬┘├───┤┌───┐ ░ ├───┤┌┴───┴┐┌───┐┌─┴─┐├─────┤»\n",
      "qr_1: |0>┤ H ├┤ H ├┤ S ├┤ X ├─┤ H ├─┤ S ├┤ Y ├─░─┤ Y ├┤ Sdg ├┤ H ├┤ X ├┤ Sdg ├»\n",
      "         └───┘└───┘└───┘└───┘ └───┘ └───┘└───┘ ░ └───┘└─────┘└───┘└───┘└─────┘»\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«      ┌───┐┌─┐        \n",
      "«qr_0: ┤ H ├┤M├────────\n",
      "«      ├───┤└╥┘┌───┐┌─┐\n",
      "«qr_1: ┤ H ├─╫─┤ H ├┤M├\n",
      "«      └───┘ ║ └───┘└╥┘\n",
      "«cr_0: ══════╩═══════╬═\n",
      "«                    ║ \n",
      "«cr_1: ══════════════╩═\n",
      "«                      \n"
     ]
    }
   ],
   "source": [
    "#Original RB circuits\n",
    "print (rb_original_circs[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         ┌───┐┌───┐          ┌─────┐┌───┐      ░       ░ ┌───┐ ┌───┐ ┌───┐┌───┐»\n",
      "qr_0: |0>┤ H ├┤ S ├───────■──┤ Sdg ├┤ H ├──────░───■───░─┤ Z ├─┤ H ├─┤ S ├┤ X ├»\n",
      "         ├───┤├───┤┌───┐┌─┴─┐└┬───┬┘├───┤┌───┐ ░ ┌─┴─┐ ░ ├───┤┌┴───┴┐├───┤└─┬─┘»\n",
      "qr_1: |0>┤ H ├┤ H ├┤ S ├┤ X ├─┤ H ├─┤ S ├┤ Y ├─░─┤ X ├─░─┤ Y ├┤ Sdg ├┤ H ├──■──»\n",
      "         └───┘└───┘└───┘└───┘ └───┘ └───┘└───┘ ░ └───┘ ░ └───┘└─────┘└───┘     »\n",
      " cr_0: 0 ══════════════════════════════════════════════════════════════════════»\n",
      "                                                                               »\n",
      " cr_1: 0 ══════════════════════════════════════════════════════════════════════»\n",
      "                                                                               »\n",
      "«           ┌───┐┌───┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├┤M├\n",
      "«      ┌─┴─┐├───┤└┬─┬┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├─┤M├──╫─\n",
      "«      └───┘└───┘ └╥┘  ║ \n",
      "«cr_0: ════════════╬═══╩═\n",
      "«                  ║     \n",
      "«cr_1: ════════════╩═════\n",
      "«                        \n"
     ]
    }
   ],
   "source": [
    "#Interleaved RB circuits\n",
    "print (rb_interleaved_circs[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a noise model for the simulator. To simulate decay, we add depolarizing error probabilities to the CNOT and U gates. Then, we execute the original and interleaved RB sequences using Qiskit Aer Simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = noise.NoiseModel()\n",
    "p1Q = 0.002\n",
    "p2Q = 0.01\n",
    "noise_model.add_all_qubit_quantum_error(depolarizing_error(p1Q, 1), 'u2')\n",
    "noise_model.add_all_qubit_quantum_error(depolarizing_error(2*p1Q, 1), 'u3')\n",
    "noise_model.add_all_qubit_quantum_error(depolarizing_error(p2Q, 2), 'cx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling seed 0\n",
      "Simulating seed 0\n",
      "Compiling seed 1\n",
      "Simulating seed 1\n",
      "Compiling seed 2\n",
      "Simulating seed 2\n",
      "Compiling seed 3\n",
      "Simulating seed 3\n",
      "Compiling seed 4\n",
      "Simulating seed 4\n",
      "Finished Simulating Original Circuits\n"
     ]
    }
   ],
   "source": [
    "#Original RB circuits\n",
    "backend = qiskit.Aer.get_backend('qasm_simulator')\n",
    "basis_gates = ['u1','u2','u3','cx'] # use U,CX for now\n",
    "shots = 200\n",
    "original_result_list = []\n",
    "original_qobj_list = []\n",
    "import time\n",
    "for rb_seed,rb_circ_seed in enumerate(rb_original_circs):\n",
    "    print('Compiling seed %d'%rb_seed)\n",
    "    new_rb_circ_seed = qiskit.compiler.transpile(rb_circ_seed, basis_gates=basis_gates)\n",
    "    qobj = qiskit.compiler.assemble(new_rb_circ_seed, shots=shots)\n",
    "    print('Simulating seed %d'%rb_seed)\n",
    "    job = backend.run(qobj, noise_model=noise_model, backend_options={'max_parallel_experiments': 0})\n",
    "    original_result_list.append(job.result())\n",
    "    original_qobj_list.append(qobj)    \n",
    "print(\"Finished Simulating Original Circuits\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling seed 0\n",
      "Simulating seed 0\n",
      "Compiling seed 1\n",
      "Simulating seed 1\n",
      "Compiling seed 2\n",
      "Simulating seed 2\n",
      "Compiling seed 3\n",
      "Simulating seed 3\n",
      "Compiling seed 4\n",
      "Simulating seed 4\n",
      "Finished Simulating Interleaved Circuits\n"
     ]
    }
   ],
   "source": [
    "#Interleaved RB circuits\n",
    "backend = qiskit.Aer.get_backend('qasm_simulator')\n",
    "basis_gates = ['u1','u2','u3','cx'] # use U,CX for now\n",
    "shots = 200\n",
    "interleaved_result_list = []\n",
    "interleaved_qobj_list = []\n",
    "import time\n",
    "for rb_seed,rb_circ_seed in enumerate(rb_interleaved_circs):\n",
    "    print('Compiling seed %d'%rb_seed)\n",
    "    new_rb_circ_seed = qiskit.compiler.transpile(rb_circ_seed, basis_gates=basis_gates)\n",
    "    qobj = qiskit.compiler.assemble(new_rb_circ_seed, shots=shots)\n",
    "    print('Simulating seed %d'%rb_seed)\n",
    "    job = backend.run(qobj, noise_model=noise_model, backend_options={'max_parallel_experiments': 0})\n",
    "    interleaved_result_list.append(job.result())\n",
    "    interleaved_qobj_list.append(qobj)    \n",
    "print(\"Finished Simulating Interleaved Circuits\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Fit the results\n",
    "\n",
    "From the values obtained for $\\alpha$ (Step 1) and $\\alpha_C$ (Step 2), the *gate error* of $\\Lambda_C$, which is exactly given\n",
    "by $r_C = 1-$average gate fidelity of $\\Lambda_C$, is estimated by:\n",
    "$ r_c^{est} = \\frac{d-1}{d}(1-\\alpha_C/\\alpha),$\n",
    "and must lie in the range $[r_C^{est}-E, r_C^{est}+E]$ where:\n",
    "$$ E = \\min \\begin{cases} \n",
    "\\frac{d-1}{d} \\bigl( |\\alpha-\\alpha_C/\\alpha|+(1-\\alpha)\\bigr) \\\\\n",
    "\\frac{2(d^2-1)(1-\\alpha)}{\\alpha d^2} + \\frac{4\\sqrt{1-\\alpha}\\sqrt{d^2-1}}{\\alpha}\n",
    "\\end{cases}.$$ \n",
    "\n",
    "As an example, we calculate the average sequence fidelity for the standard and interleaved RB sequences, fit the results to the exponential curve, and compute the paraemters $\\alpha$, $\\alpha_C$, epc (=$r$) and epc_est (=$r_C^{est}$),\n",
    "as well as the *systemtic error* $E$ and the bounds systematic_err_L = $r_C^{est}-E$ and systematic_err_R = $r_C^{est}+E$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Create the original and interleaved RB fitter\n",
    "original_rb_fit = rb.RBFitter(original_result_list, xdata, rb_opts['rb_pattern'])\n",
    "interleaved_rb_fit = rb.RBFitter(interleaved_result_list, xdata, rb_opts['rb_pattern'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'alpha': 0.982466214495266, 'alpha_err': 0.0014392100251542014, 'alpha_c': 0.9704497593230009, 'alpha_c_err': 0.00163780215693106, 'epc_est': 0.00917318198451117, 'epc_est_err': 0.0016555712734152603, 'systematic_err': 0.01712749627258975, 'systematic_err_L': -0.007954314288078579, 'systematic_err_R': 0.026300678257100918}]\n"
     ]
    }
   ],
   "source": [
    "#Calculate the joint fitter\n",
    "joint_rb_fit = rb.InterleavedRBFitter(original_result_list, interleaved_result_list, xdata, rb_opts['rb_pattern'])\n",
    "print (joint_rb_fit.fit_int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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md2zcuJEzZ864WH7fvHmTtWvXMnnyZC5dukR8fDwiQlRUVCIlwf5g/u677xzT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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3c3f619b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "ax = plt.subplot(1, 1, 1)\n",
    "\n",
    "# Plot the essence by calling plot_rb_data\n",
    "joint_rb_fit.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)\n",
    "    \n",
    "# Add title and label\n",
    "ax.set_title('%d Qubit Interleaved RB'%(nQ), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Purity RB protocol\n",
    "\n",
    "**Purity RB** quantifies how coherent the errors are. The protocol executes the RB sequneces containing of Clifford gates, and then calculates the purity $Tr(\\rho^2)$, and fits the purity result to an exponentially decaying curve.\n",
    "If the noise is coherent then necessarily $Tr(\\rho^2)=1$.\n",
    "\n",
    "### Definition of the purity\n",
    "The purity is defined as \n",
    "$$\n",
    "\\mathcal{P}  = {Tr}(\\rho^2)\n",
    "$$\n",
    "where $\\rho$ can be expressed as a sum of Pauli matrices\n",
    "$$\n",
    "\\rho = \\sum_{i} \\alpha_i P_i\n",
    "$$\n",
    "where $i$ is a sum over $4^n$ Paulis. Therefore,\n",
    "$$\n",
    "\\rho^2 = \\sum_{ij} \\alpha_i \\alpha_j P_i \\cdot P_j\n",
    "$$\n",
    "and\n",
    "$$\n",
    "Tr(\\rho^2) = \\sum_{ij} \\alpha_i \\alpha_j Tr(P_i P_j)\n",
    "$$\n",
    "If $i\\ne j$ then $P_i P_j = P_k$ (where $P_k \\ne \\mathbf{I}$ and if $i==j$ then $P_i P_j = \\mathcal{I}$). Since $Tr(P_k)=0$, then\n",
    "$$\n",
    "Tr(\\rho^2) = \\sum_i \\alpha_i^2 d\n",
    "$$\n",
    "Now we can calculate any expectation value as,\n",
    "$$\n",
    "\\langle \\hat{A} \\rangle = Tr(\\hat{A} \\rho)\n",
    "$$\n",
    "so the Pauli expectation value is\n",
    "$$\n",
    "\\langle P_k \\rangle  =  Tr(P_k \\rho) \n",
    " =  \\sum_i \\alpha_i Tr(P_k P_i)\n",
    " =  \\alpha_k d\n",
    "$$\n",
    "so\n",
    "$$\n",
    "Tr(\\rho^2) = \\sum_k \\langle P_k \\rangle^2 /d\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Generating the purity RB sequences \n",
    "\n",
    "To calculate all $Z$ correlators we only need the on diagonal elements of $\\rho$ (i.e. what is measured in experiment). If we apply a $\\pi/2$ rotation to the density matrix and then measure the $Z$ correlator,\n",
    "$$\n",
    "\\rho^{'}  =  e^{i P_j \\pi/4} \\rho e^{-i P_j \\pi/4} \n",
    "$$\n",
    "$$\n",
    "Tr(Z \\rho^{'})  =  Tr(Z e^{i P_j \\pi/4} \\rho e^{-i P_j \\pi/4}) \n",
    " =  Tr(e^{-i P_j \\pi/4}Z e^{i P_j \\pi/4} \\rho)\n",
    "$$\n",
    "which looks like calculating the expectation value of the rotated Pauli. \n",
    "\n",
    "Therefore, in order to generate each of the $3^n$ circuits, we need to do (per each of the $n$ qubits) either:\n",
    "- nothing (Pauli-$Z$), or\n",
    "- $\\pi/2$-rotation around $x$ (Pauli-$X$), or\n",
    "- $\\pi/2$-rotation around $y$ (Pauli-$Y$),\n",
    "\n",
    "and then measure the result.\n",
    "\n",
    "For example, we generate below sequences of 2-qubit Clifford purity circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    }
   ],
   "source": [
    "# Example of 2-qubits Purity RB\n",
    "#Number of qubits\n",
    "nQ = 2\n",
    "rb_opts = {}\n",
    "#Number of Cliffords in the sequence (start, stop, steps)\n",
    "rb_opts['length_vector'] = np.arange(1,200,20)\n",
    "#Number of seeds (random sequences)\n",
    "rb_opts['nseeds'] = 1\n",
    "#Default pattern\n",
    "rb_opts['rb_pattern'] = [[0,1]]\n",
    "#Parameter for purity RB\n",
    "rb_opts['is_purity'] = True\n",
    "rb_purity_circs, xdata, npurity = rb.randomized_benchmarking_seq(**rb_opts)\n",
    "print (npurity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To illustrate, we print the circuit names for purity RB (for length=0 and seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rb_purity_ZZ_length_0_seed_0\n",
      "rb_purity_XZ_length_0_seed_0\n",
      "rb_purity_YZ_length_0_seed_0\n",
      "rb_purity_ZX_length_0_seed_0\n",
      "rb_purity_XX_length_0_seed_0\n",
      "rb_purity_YX_length_0_seed_0\n",
      "rb_purity_ZY_length_0_seed_0\n",
      "rb_purity_XY_length_0_seed_0\n",
      "rb_purity_YY_length_0_seed_0\n"
     ]
    }
   ],
   "source": [
    "for j in range(len(rb_purity_circs[0])):\n",
    "    print (rb_purity_circs[0][j][0].name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we print the circuits corresponding to the first RB sequences, for each of the $3^n$ parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "circ no.  0\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐┌───┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├┤ H ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤└┬─┬┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├─┤M├──╫─\n",
      "«      └───┘└───┘└───┘ └╥┘  ║ \n",
      "«cr_0: ═════════════════╬═══╩═\n",
      "«                       ║     \n",
      "«cr_1: ═════════════════╩═════\n",
      "«                             \n",
      "circ no.  1\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐┌───┐┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├┤ H ├┤ Rx(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤└┬─┬┘└────────────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├─┤M├────────────────╫─\n",
      "«      └───┘└───┘└───┘ └╥┘                ║ \n",
      "«cr_0: ═════════════════╬═════════════════╩═\n",
      "«                       ║                   \n",
      "«cr_1: ═════════════════╩═══════════════════\n",
      "«                                           \n",
      "circ no.  2\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐┌───┐┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├┤ H ├┤ Ry(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤└┬─┬┘└────────────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├─┤M├────────────────╫─\n",
      "«      └───┘└───┘└───┘ └╥┘                ║ \n",
      "«cr_0: ═════════════════╬═════════════════╩═\n",
      "«                       ║                   \n",
      "«cr_1: ═════════════════╩═══════════════════\n",
      "«                                           \n",
      "circ no.  3\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌─┐   \n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤M├───\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└╥┘┌─┐\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Rx(1.5708) ├─╫─┤M├\n",
      "«      └───┘└───┘└───┘└────────────┘ ║ └╥┘\n",
      "«cr_0: ══════════════════════════════╩══╬═\n",
      "«                                       ║ \n",
      "«cr_1: ═════════════════════════════════╩═\n",
      "«                                         \n",
      "circ no.  4\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤ Rx(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└────┬─┬─────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Rx(1.5708) ├─────┤M├───────╫─\n",
      "«      └───┘└───┘└───┘└────────────┘     └╥┘       ║ \n",
      "«cr_0: ═══════════════════════════════════╬════════╩═\n",
      "«                                         ║          \n",
      "«cr_1: ═══════════════════════════════════╩══════════\n",
      "«                                                    \n",
      "circ no.  5\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤ Ry(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└────┬─┬─────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Rx(1.5708) ├─────┤M├───────╫─\n",
      "«      └───┘└───┘└───┘└────────────┘     └╥┘       ║ \n",
      "«cr_0: ═══════════════════════════════════╬════════╩═\n",
      "«                                         ║          \n",
      "«cr_1: ═══════════════════════════════════╩══════════\n",
      "«                                                    \n",
      "circ no.  6\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌─┐   \n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤M├───\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└╥┘┌─┐\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Ry(1.5708) ├─╫─┤M├\n",
      "«      └───┘└───┘└───┘└────────────┘ ║ └╥┘\n",
      "«cr_0: ══════════════════════════════╩══╬═\n",
      "«                                       ║ \n",
      "«cr_1: ═════════════════════════════════╩═\n",
      "«                                         \n",
      "circ no.  7\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤ Rx(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└────┬─┬─────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Ry(1.5708) ├─────┤M├───────╫─\n",
      "«      └───┘└───┘└───┘└────────────┘     └╥┘       ║ \n",
      "«cr_0: ═══════════════════════════════════╬════════╩═\n",
      "«                                         ║          \n",
      "«cr_1: ═══════════════════════════════════╩══════════\n",
      "«                                                    \n",
      "circ no.  8\n",
      "          ┌───┐ ┌─────┐┌───┐     ┌───┐┌─────┐┌───┐┌───┐ ░ ┌───┐┌───┐┌───┐┌───┐»\n",
      "qr_0: |0>─┤ H ├─┤ Sdg ├┤ H ├──■──┤ X ├┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├┤ X ├»\n",
      "         ┌┴───┴┐└┬───┬┘└───┘┌─┴─┐└─┬─┘├─────┤├───┤├───┤ ░ ├───┤├───┤├───┤└─┬─┘»\n",
      "qr_1: |0>┤ Sdg ├─┤ H ├──────┤ X ├──■──┤ Sdg ├┤ H ├┤ Y ├─░─┤ Y ├┤ H ├┤ S ├──■──»\n",
      "         └─────┘ └───┘      └───┘     └─────┘└───┘└───┘ ░ └───┘└───┘└───┘     »\n",
      " cr_0: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      " cr_1: 0 ═════════════════════════════════════════════════════════════════════»\n",
      "                                                                              »\n",
      "«           ┌───┐┌───┐    ┌───┐     ┌────────────┐┌─┐\n",
      "«qr_0: ──■──┤ H ├┤ S ├────┤ H ├─────┤ Ry(1.5708) ├┤M├\n",
      "«      ┌─┴─┐├───┤├───┤┌───┴───┴────┐└────┬─┬─────┘└╥┘\n",
      "«qr_1: ┤ X ├┤ H ├┤ S ├┤ Ry(1.5708) ├─────┤M├───────╫─\n",
      "«      └───┘└───┘└───┘└────────────┘     └╥┘       ║ \n",
      "«cr_0: ═══════════════════════════════════╬════════╩═\n",
      "«                                         ║          \n",
      "«cr_1: ═══════════════════════════════════╩══════════\n",
      "«                                                    \n"
     ]
    }
   ],
   "source": [
    "for i in range(npurity):\n",
    "    print (\"circ no. \", i)\n",
    "    print (rb_purity_circs[0][i][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a noise model for the simulator. To simulate decay, we add depolarizing error probabilities to the CNOT gate. Then, we execute the purity RB sequences using Qiskit Aer Simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Executing seed 0 purity 0 length 10\n",
      "Executing seed 0 purity 1 length 10\n",
      "Executing seed 0 purity 2 length 10\n",
      "Executing seed 0 purity 3 length 10\n",
      "Executing seed 0 purity 4 length 10\n",
      "Executing seed 0 purity 5 length 10\n",
      "Executing seed 0 purity 6 length 10\n",
      "Executing seed 0 purity 7 length 10\n",
      "Executing seed 0 purity 8 length 10\n",
      "Finished Simulating Purity RB Circuits\n"
     ]
    }
   ],
   "source": [
    "#Non-coherent noise model - depolarizing noise\n",
    "noise_model = noise.NoiseModel()\n",
    "p2Q = 0.01\n",
    "noise_model.add_all_qubit_quantum_error(depolarizing_error(p2Q, 2), 'cx')\n",
    "\n",
    "#Execute purity RB circuits \n",
    "backend = qiskit.Aer.get_backend('qasm_simulator')\n",
    "basis_gates = ['u1','u2','u3','cx'] # use U,CX for now\n",
    "shots = 200\n",
    "purity_result_list = []\n",
    "import time\n",
    "for rb_seed in range(len(rb_purity_circs)):\n",
    "    for d in range(npurity):\n",
    "        print('Executing seed %d purity %d length %d'%(rb_seed, d, len(rb_opts['length_vector'])))\n",
    "        new_circ = rb_purity_circs[rb_seed][d]\n",
    "        job = qiskit.execute(new_circ, backend=backend, noise_model=noise_model, shots=shots, basis_gates=['u1','u2','u3','cx'])\n",
    "        purity_result_list.append(job.result())\n",
    "print(\"Finished Simulating Purity RB Circuits\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Calculating the purity $Tr(\\rho^2)$\n",
    "\n",
    "We made $3^n$ experiments and got $2^n$ expectation values per experiment (total of $6^n$ expectation values).\n",
    "\n",
    "For example, for $n=2$ we get the following $4$ expectation values per each of the $9$ experiments:\n",
    "\n",
    "Purity_ZZ: $\\langle II \\rangle$ $ \\langle IZ \\rangle$ $ \\langle ZI \\rangle$ $ \\langle ZZ \\rangle$\n",
    "\n",
    "Purity_XZ: $\\langle II \\rangle$ $ \\langle IZ \\rangle$ $ \\langle XI \\rangle$ $ \\langle XZ \\rangle$\n",
    "\n",
    "Purity_YZ: $\\langle II \\rangle$ $ \\langle IZ \\rangle$ $ \\langle YI \\rangle$ $ \\langle YZ \\rangle$\n",
    "\n",
    "Purity_ZX: $\\langle II \\rangle$ $ \\langle IX \\rangle$ $ \\langle ZI \\rangle$ $ \\langle ZX \\rangle$\n",
    "\n",
    "Purity_ZY: $\\langle II \\rangle$ $ \\langle IY \\rangle$ $ \\langle ZI \\rangle$ $ \\langle ZY \\rangle$ \n",
    "\n",
    "Purity_XX: $\\langle II \\rangle$ $ \\langle IX \\rangle$ $ \\langle XI \\rangle$ $ \\langle XX \\rangle$ \n",
    "\n",
    "Purity_XY: $\\langle II \\rangle$ $ \\langle IY \\rangle$ $ \\langle XI \\rangle$ $ \\langle XY \\rangle$ \n",
    "\n",
    "Purity_YX: $\\langle II \\rangle$ $ \\langle IX \\rangle$ $ \\langle YI \\rangle$ $ \\langle YX \\rangle$\n",
    "\n",
    "Purity_YY: $\\langle II \\rangle$ $ \\langle IY \\rangle$ $ \\langle YI \\rangle$ $ \\langle YY \\rangle$\n",
    "\n",
    "So, the purity is defined as the following sum of $16=4^n$ squares (divided by $4=2^n$):\n",
    "$$\\bigl( 1 + (\\Sigma \\langle IZ \\rangle/3)^2 + (\\Sigma \\langle IY \\rangle/3)^2 + (\\Sigma \\langle IX \\rangle/3)^2 + (\\Sigma \\langle ZI \\rangle/3)^2 + (\\Sigma \\langle XI\\rangle/3)^2 + (\\Sigma \\langle YI\\rangle/3)^2 + \\\\ \n",
    "\\langle ZZ\\rangle^2 + \\langle XZ\\rangle^2 + \\langle YZ\\rangle^2 + \\langle ZX\\rangle^2 + \\langle ZY\\rangle^2 + \\langle XX\\rangle^2 + \\langle XY\\rangle^2 + \\langle YX\\rangle^2 + \\langle YY\\rangle^2 \\bigr) / 4$$\n",
    "Since $\\langle II\\rangle=1$, and  $\\langle IZ\\rangle,\\langle IY\\rangle,\\langle IX\\rangle,\\langle ZI\\rangle,\\langle XI\\rangle,\\langle YI\\rangle$ appear 3 times each."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Fit the results\n",
    "\n",
    "According to [3], assuming pure depolarizing noise $\\alpha$, the density matrix after $m$ Cliffords (starting in the ground state density matrix $\\rho_0$) is \n",
    "$$ \\rho(m) = \\alpha^m \\rho_0 + (1-\\alpha^m)\\frac{\\mathcal{I}}{d},$$\n",
    "So\n",
    "$$ \\rho^2(m) = \\alpha^{2m} \\rho^2_0 + (1-\\alpha^m)^2\\frac{\\mathcal{I}}{d^2} + 2\\alpha^m(1-\\alpha^m)\\frac{\\rho_0}{d},$$\n",
    "Then\n",
    "$$Tr(\\rho^2[m]) = (1-1/d)\\alpha^{2m} + 1/d.$$\n",
    "\n",
    "Therefore, we fit the data to $A\\alpha^{2m} + B$ and label the quantity $\\frac{d-1}{d} (1-\\alpha)$\n",
    "as the *purity error per Clifford gate (PEPC)*.\n",
    "\n",
    "As an example, we calculate $Tr(\\rho^2)$ as described above, fit the results to the exponential curve, and compute the paraemters $\\alpha$ and PEPC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fit: [{'params': array([0.70933013, 0.98727468, 0.25698225]), 'params_err': array([0.01259387, 0.0005551 , 0.00740674]), 'epc': 0.018966529835729523, 'epc_err': 0.0008488066578079781, 'pepc': 0.00954399008232576, 'pepc_err': 0.0004216943490439854}]\n"
     ]
    }
   ],
   "source": [
    "rbfit_purity = rb.PurityRBFitter(purity_result_list, npurity, xdata, rb_opts['rb_pattern'])\n",
    "print (\"fit:\", rbfit_purity.fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e7naeBQsWcOWVV2b6rAMRcbdMTJs2jerVq7tPvidPnkzXaz95Pm0LwJo1a/jl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff35ea81470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "ax = plt.subplot(1, 1, 1)\n",
    "\n",
    "# Plot the essence by calling plot_rb_data\n",
    "rbfit_purity.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)\n",
    "    \n",
    "# Add title and label\n",
    "ax.set_title('%d Qubit Purity RB'%(nQ), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard RB results\n",
    "\n",
    "For comparison, we also print the standard RB fit results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "standard_result_list = []\n",
    "count = 0\n",
    "for rb_seed in range(len(rb_purity_circs)):\n",
    "    for d in range(npurity):\n",
    "        if d==0:\n",
    "            standard_result_list.append(purity_result_list[count])\n",
    "        count += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'params': array([0.73643956, 0.98635037, 0.24610225]), 'params_err': array([0.04348855, 0.00226793, 0.04557745]), 'epc': 0.010237225630939234, 'epc_err': 0.0017244838515169812}]\n"
     ]
    }
   ],
   "source": [
    "rbfit_standard = rb.RBFitter(standard_result_list, xdata, rb_opts['rb_pattern'])\n",
    "print (rbfit_standard.fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FFVewb98+Bg4cSLt27dz7vf38+oq1APjSsGHgelb0bvDjHNv1L0n+fpsUDhw4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff35ed41470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "ax = plt.subplot(1, 1, 1)\n",
    "\n",
    "# Plot the essence by calling plot_rb_data\n",
    "rbfit_standard.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)\n",
    "    \n",
    "# Add title and label\n",
    "ax.set_title('%d Qubit Standard RB'%(nQ), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define a coherent noise model\n",
    "\n",
    "We define a coherent noise model for the simulator. In this example we expect the purity RB to measure no errors, but standard RB will still measure a non-zero error.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Coherent noise model\n",
    "err_unitary = np.zeros([2, 2], dtype=complex)\n",
    "angle_err = 0.1\n",
    "for i in range(2):\n",
    "    err_unitary[i, i] = np.cos(angle_err)\n",
    "    err_unitary[i, (i+1) % 2] = np.sin(angle_err)\n",
    "err_unitary[0, 1] *= -1.0\n",
    "\n",
    "error = coherent_unitary_error(err_unitary)\n",
    "noise_model = noise.NoiseModel()\n",
    "noise_model.add_all_qubit_quantum_error(error, 'u3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Executing seed 0 purity 0 length 10\n",
      "Executing seed 0 purity 1 length 10\n",
      "Executing seed 0 purity 2 length 10\n",
      "Executing seed 0 purity 3 length 10\n",
      "Executing seed 0 purity 4 length 10\n",
      "Executing seed 0 purity 5 length 10\n",
      "Executing seed 0 purity 6 length 10\n",
      "Executing seed 0 purity 7 length 10\n",
      "Executing seed 0 purity 8 length 10\n",
      "Finished Simulating Purity RB Circuits\n"
     ]
    }
   ],
   "source": [
    "#Execute purity RB circuits \n",
    "backend = qiskit.Aer.get_backend('qasm_simulator')\n",
    "basis_gates = ['u1','u2','u3','cx'] # use U,CX for now\n",
    "shots = 200\n",
    "coherent_purity_result_list = []\n",
    "import time\n",
    "for rb_seed in range(len(rb_purity_circs)):\n",
    "    for d in range(npurity):\n",
    "        print('Executing seed %d purity %d length %d'%(rb_seed, d, len(rb_opts['length_vector'])))\n",
    "        new_circ = rb_purity_circs[rb_seed][d]\n",
    "        job = qiskit.execute(new_circ, backend=backend, shots=shots, noise_model=noise_model, basis_gates=['u1','u2','u3','cx'])\n",
    "        coherent_purity_result_list.append(job.result())\n",
    "print(\"Finished Simulating Purity RB Circuits\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fit: [{'params': array([0.63447252, 1.        , 0.39394026]), 'params_err': array([0.02439911, 0.00035735, 0.02439911]), 'epc': 2.3564483697668948e-14, 'epc_err': 0.0005360186624963699, 'pepc': 1.1823875212257917e-14, 'pepc_err': 0.0002680093312481829}]\n"
     ]
    }
   ],
   "source": [
    "rbfit_purity = rb.PurityRBFitter(coherent_purity_result_list, npurity, xdata, rb_opts['rb_pattern'])\n",
    "print (\"fit:\", rbfit_purity.fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ccMEFAZ/32LFjfPHFF/Tv3z/bd9OmTRvGjBlD3bp1cxyG9Pc9tG3blokTJ3Ld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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff35efe3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "ax = plt.subplot(1, 1, 1)\n",
    "\n",
    "# Plot the essence by calling plot_rb_data\n",
    "rbfit_purity.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)\n",
    "    \n",
    "# Add title and label\n",
    "ax.set_title('%d Qubit Purity RB'%(nQ), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard RB results\n",
    "\n",
    "For comparison, we also print the standard RB fit results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "standard_result_list = []\n",
    "count = 0\n",
    "for rb_seed in range(len(rb_purity_circs)):\n",
    "    for d in range(npurity):\n",
    "        if d==0:\n",
    "            standard_result_list.append(coherent_purity_result_list[count])\n",
    "        count += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'params': array([ 2.        ,  0.99745721, -1.11840812]), 'params_err': array([4.23902956, 0.0068336 , 4.30400632]), 'epc': 0.0019070891726288008, 'epc_err': 0.005138262027875257}]\n"
     ]
    }
   ],
   "source": [
    "rbfit_standard = rb.RBFitter(standard_result_list, xdata, rb_opts['rb_pattern'])\n",
    "print (rbfit_standard.fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RqlSpQoECBWjevDkvvvgiJUuWpGDBgvz3339cuHCB4OBgl59FeHg4JUqUYPfu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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff35e4a9fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "ax = plt.subplot(1, 1, 1)\n",
    "\n",
    "# Plot the essence by calling plot_rb_data\n",
    "rbfit_standard.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)\n",
    "    \n",
    "# Add title and label\n",
    "ax.set_title('%d Qubit Standard RB'%(nQ), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
